I appreciate all the comments and suggestions. My shoes are an old pair of Diadora that I've had for at least 20 years and I noticed that my toes lightly touch the end. I stopped by the bike shop last night to look at toe covers and got a pair by Castelli, and by chance they had a pair of Sidi shoes on sale that are one size larger than my old shoes, so I got them too. I also got a pack of toe warmers to try.

Now I need to find some wool socks.

One way or another, I intend to solve this problem.